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#### Question

Establish the following vector inequalities geometrically or otherwise:

(a) |**a ***+ ***b**| ≤ |**a**| + |**b**|

(b) |**a ***+ ***b**| ≥ ||**a**| − |**b**||

(c) |**a ***− ***b**| ≤ |**a**| + |**b**|

(d) |**a ***− ***b**| ≥ ||**a**| − |**b**||

When does the equality sign above apply?

#### Solution

#### Similar questions

Three girls skating on a circular ice ground of radius 200 m start from a point Pon the edge of the ground and reach a point Qdiametrically opposite to P following different paths as shown in Figure. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?

Read each statement below carefully and state with reasons, if it is true or false:

The magnitude of a vector is always a scalar

Read each statement below carefully and state with reasons, if it is true or false:

the total path length is always equal to the magnitude of the displacement vector of a particle.

Pick out the only vector quantity in the following list:

Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.

State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.